Abstract

The size and edge-dependence of two-photon absorption (TPA) for rectangular graphene quantum dots (GQDs) is investigated theoretically in the framework of Dirac equation under hard wall boundary conditions. The TPA cross section associated with interband transitions around K point is derived and the transition selection rules are obtained. Results reveal that when the size of zigzag-edge M = 3M0 ± 1 (M0 is an integer), the GQD exhibits a semiconductor while for M = 3M0 it is metallic. For semiconducting rectangular GQDs, TPA is tuned by the sizes of both edges in GQDs and the armchair-edge dimension contributes more to TPA. While for metallic rectangular GQDs, zigzag-edge dimension affects TPA little and the position of absorption peak and the magnitude of the TPA coefficient are determined by the size of armchair-edge and the resonant enhancement occurs.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. P. Suvarnaphaet and S. Pechprasarn, “Graphene-based materials for biosensors: a review,” Sensors 17(10), 2161 (2017).
  2. H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
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  3. J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
    [Crossref] [PubMed]
  4. Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
    [Crossref]
  5. A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
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  6. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
    [Crossref] [PubMed]
  7. C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
    [Crossref] [PubMed]
  8. D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
    [Crossref] [PubMed]
  9. Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
    [Crossref] [PubMed]
  10. X. T. Zheng, A. Ananthanarayanan, K. Q. Luo, and P. Chen, “Glowing graphene quantum dots and carbon dots: properties, syntheses, and biological applications,” Small 11(14), 1620–1636 (2015).
    [Crossref] [PubMed]
  11. S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
    [Crossref] [PubMed]
  12. Q. Liu, B. Guo, Z. Rao, B. Zhang, and J. R. Gong, “Strong two-photon-induced fluorescence from photostable, biocompatible nitrogen-doped graphene quantum dots for cellular and deep-tissue imaging,” Nano Lett. 13(6), 2436–2441 (2013).
    [Crossref] [PubMed]
  13. M. Ghaffarian and F. Ebrahimi, “The linear and nonlinear optical properties of trigonal zigzag graphene nanoflakes,” Phys. Scr. 88(2), 025703 (2013).
    [Crossref]
  14. R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).
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    [Crossref]
  16. X. Feng, X. Li, Z. Li, and Y. Liu, “Size-dependent two-photon absorption in circular graphene quantum dots,” Opt. Express 24(3), 2877–2884 (2016).
    [Crossref] [PubMed]
  17. X. Feng, Z. Li, X. Li, and Y. Liu, “Giant Two-photon Absorption in Circular Graphene Quantum Dots in Infrared Region,” Sci. Rep. 6(6), 33260 (2016).
    [Crossref] [PubMed]
  18. T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: Phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78(20), 205403 (2008).
    [Crossref]
  19. T. Ando and T. Nakanishi, “Impurity Scattering in Carbon Nanotubes Absence of Back Scattering,” J. Phys. Soc. Jpn. 67(67), 1704–1713 (1998).
    [Crossref]
  20. J. Qian, M. Dutta, and M. A. Stroscio, “Phonon bottleneck effects in rectangular graphene quantum dots,” J. Comput. Electron. 11(3), 293–301 (2012).
    [Crossref]
  21. B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3(3), 192–196 (2007).
    [Crossref]
  22. P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene,” Phys. Rev. Lett. 98(1), 016802 (2007).
    [Crossref] [PubMed]
  23. F. C. Salomão, E. Lanzoni, C. Costa, C. Deneke, and E. B. Barros, “Determination of high frequency dielectric constant and surface potential of graphene oxide and influence of humidity by KPFM,” Languir 31(41), 11339–11343 (2015).
    [Crossref] [PubMed]
  24. X. Feng and W. Ji, “Shape-dependent two-photon absorption in semiconductor nanocrystals,” Opt. Express 17(15), 13140–13150 (2009).
    [Crossref] [PubMed]

2017 (1)

P. Suvarnaphaet and S. Pechprasarn, “Graphene-based materials for biosensors: a review,” Sensors 17(10), 2161 (2017).

2016 (4)

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

X. Feng, X. Li, Z. Li, and Y. Liu, “Size-dependent two-photon absorption in circular graphene quantum dots,” Opt. Express 24(3), 2877–2884 (2016).
[Crossref] [PubMed]

X. Feng, Z. Li, X. Li, and Y. Liu, “Giant Two-photon Absorption in Circular Graphene Quantum Dots in Infrared Region,” Sci. Rep. 6(6), 33260 (2016).
[Crossref] [PubMed]

2015 (3)

X. T. Zheng, A. Ananthanarayanan, K. Q. Luo, and P. Chen, “Glowing graphene quantum dots and carbon dots: properties, syntheses, and biological applications,” Small 11(14), 1620–1636 (2015).
[Crossref] [PubMed]

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

F. C. Salomão, E. Lanzoni, C. Costa, C. Deneke, and E. B. Barros, “Determination of high frequency dielectric constant and surface potential of graphene oxide and influence of humidity by KPFM,” Languir 31(41), 11339–11343 (2015).
[Crossref] [PubMed]

2013 (3)

F. Qi and G. Jin, “Strain sensing and far-infrared absorption in strained graphene quantum dots,” J. Appl. Phys. 114(7), 073509 (2013).
[Crossref]

Q. Liu, B. Guo, Z. Rao, B. Zhang, and J. R. Gong, “Strong two-photon-induced fluorescence from photostable, biocompatible nitrogen-doped graphene quantum dots for cellular and deep-tissue imaging,” Nano Lett. 13(6), 2436–2441 (2013).
[Crossref] [PubMed]

M. Ghaffarian and F. Ebrahimi, “The linear and nonlinear optical properties of trigonal zigzag graphene nanoflakes,” Phys. Scr. 88(2), 025703 (2013).
[Crossref]

2012 (3)

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

J. Qian, M. Dutta, and M. A. Stroscio, “Phonon bottleneck effects in rectangular graphene quantum dots,” J. Comput. Electron. 11(3), 293–301 (2012).
[Crossref]

2009 (3)

X. Feng and W. Ji, “Shape-dependent two-photon absorption in semiconductor nanocrystals,” Opt. Express 17(15), 13140–13150 (2009).
[Crossref] [PubMed]

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

2008 (1)

T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: Phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78(20), 205403 (2008).
[Crossref]

2007 (2)

B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3(3), 192–196 (2007).
[Crossref]

P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene,” Phys. Rev. Lett. 98(1), 016802 (2007).
[Crossref] [PubMed]

2006 (1)

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

2005 (1)

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

1998 (1)

T. Ando and T. Nakanishi, “Impurity Scattering in Carbon Nanotubes Absence of Back Scattering,” J. Phys. Soc. Jpn. 67(67), 1704–1713 (1998).
[Crossref]

Ananthanarayanan, A.

X. T. Zheng, A. Ananthanarayanan, K. Q. Luo, and P. Chen, “Glowing graphene quantum dots and carbon dots: properties, syntheses, and biological applications,” Small 11(14), 1620–1636 (2015).
[Crossref] [PubMed]

Ando, T.

T. Ando and T. Nakanishi, “Impurity Scattering in Carbon Nanotubes Absence of Back Scattering,” J. Phys. Soc. Jpn. 67(67), 1704–1713 (1998).
[Crossref]

Ashrafi, M.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Bae, S.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Bao, Q.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

Barros, E. B.

F. C. Salomão, E. Lanzoni, C. Costa, C. Deneke, and E. B. Barros, “Determination of high frequency dielectric constant and surface potential of graphene oxide and influence of humidity by KPFM,” Languir 31(41), 11339–11343 (2015).
[Crossref] [PubMed]

Berger, C.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Brown, N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Bulaev, D. V.

B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3(3), 192–196 (2007).
[Crossref]

Burkard, G.

B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3(3), 192–196 (2007).
[Crossref]

Chen, P.

X. T. Zheng, A. Ananthanarayanan, K. Q. Luo, and P. Chen, “Glowing graphene quantum dots and carbon dots: properties, syntheses, and biological applications,” Small 11(14), 1620–1636 (2015).
[Crossref] [PubMed]

Choi, H. J.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Choi, S. H.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Conrad, E. H.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Costa, C.

F. C. Salomão, E. Lanzoni, C. Costa, C. Deneke, and E. B. Barros, “Determination of high frequency dielectric constant and surface potential of graphene oxide and influence of humidity by KPFM,” Languir 31(41), 11339–11343 (2015).
[Crossref] [PubMed]

de Heer, W. A.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Deneke, C.

F. C. Salomão, E. Lanzoni, C. Costa, C. Deneke, and E. B. Barros, “Determination of high frequency dielectric constant and surface potential of graphene oxide and influence of humidity by KPFM,” Languir 31(41), 11339–11343 (2015).
[Crossref] [PubMed]

Dhanabalan, S. C.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Dimiev, A.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Dutta, M.

J. Qian, M. Dutta, and M. A. Stroscio, “Phonon bottleneck effects in rectangular graphene quantum dots,” J. Comput. Electron. 11(3), 293–301 (2012).
[Crossref]

Ebrahimi, F.

M. Ghaffarian and F. Ebrahimi, “The linear and nonlinear optical properties of trigonal zigzag graphene nanoflakes,” Phys. Scr. 88(2), 025703 (2013).
[Crossref]

Efetov, K. B.

P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene,” Phys. Rev. Lett. 98(1), 016802 (2007).
[Crossref] [PubMed]

Fang, T.

T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: Phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78(20), 205403 (2008).
[Crossref]

Feng, X.

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

First, P. N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Geim, A. K.

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Ghaffarian, M.

M. Ghaffarian and F. Ebrahimi, “The linear and nonlinear optical properties of trigonal zigzag graphene nanoflakes,” Phys. Scr. 88(2), 025703 (2013).
[Crossref]

Godbout, N.

Gong, J. R.

Q. Liu, B. Guo, Z. Rao, B. Zhang, and J. R. Gong, “Strong two-photon-induced fluorescence from photostable, biocompatible nitrogen-doped graphene quantum dots for cellular and deep-tissue imaging,” Nano Lett. 13(6), 2436–2441 (2013).
[Crossref] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Guo, B.

Q. Liu, B. Guo, Z. Rao, B. Zhang, and J. R. Gong, “Strong two-photon-induced fluorescence from photostable, biocompatible nitrogen-doped graphene quantum dots for cellular and deep-tissue imaging,” Nano Lett. 13(6), 2436–2441 (2013).
[Crossref] [PubMed]

Guo, Z.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Hass, J.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Higginbotham, A. L.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Hong, B. H.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Huang, H.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Hwang, E.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Hwang, S. W.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Jena, D.

T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: Phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78(20), 205403 (2008).
[Crossref]

Ji, W.

Jia, J.

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Jin, G.

F. Qi and G. Jin, “Strain sensing and far-infrared absorption in strained graphene quantum dots,” J. Appl. Phys. 114(7), 073509 (2013).
[Crossref]

Kim, C. O.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Kim, M. K.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Kim, P.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Kim, S.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Ko, G.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Kockaert, P.

Konar, A.

T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: Phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78(20), 205403 (2008).
[Crossref]

Kosynkin, D. V.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Lanzoni, E.

F. C. Salomão, E. Lanzoni, C. Costa, C. Deneke, and E. B. Barros, “Determination of high frequency dielectric constant and surface potential of graphene oxide and influence of humidity by KPFM,” Languir 31(41), 11339–11343 (2015).
[Crossref] [PubMed]

Li, P.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Li, S.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Li, T.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Li, X.

X. Feng, X. Li, Z. Li, and Y. Liu, “Size-dependent two-photon absorption in circular graphene quantum dots,” Opt. Express 24(3), 2877–2884 (2016).
[Crossref] [PubMed]

X. Feng, Z. Li, X. Li, and Y. Liu, “Giant Two-photon Absorption in Circular Graphene Quantum Dots in Infrared Region,” Sci. Rep. 6(6), 33260 (2016).
[Crossref] [PubMed]

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Li, Z.

X. Feng, Z. Li, X. Li, and Y. Liu, “Giant Two-photon Absorption in Circular Graphene Quantum Dots in Infrared Region,” Sci. Rep. 6(6), 33260 (2016).
[Crossref] [PubMed]

X. Feng, X. Li, Z. Li, and Y. Liu, “Size-dependent two-photon absorption in circular graphene quantum dots,” Opt. Express 24(3), 2877–2884 (2016).
[Crossref] [PubMed]

Liu, Q.

Q. Liu, B. Guo, Z. Rao, B. Zhang, and J. R. Gong, “Strong two-photon-induced fluorescence from photostable, biocompatible nitrogen-doped graphene quantum dots for cellular and deep-tissue imaging,” Nano Lett. 13(6), 2436–2441 (2013).
[Crossref] [PubMed]

Liu, Y.

X. Feng, Z. Li, X. Li, and Y. Liu, “Giant Two-photon Absorption in Circular Graphene Quantum Dots in Infrared Region,” Sci. Rep. 6(6), 33260 (2016).
[Crossref] [PubMed]

X. Feng, X. Li, Z. Li, and Y. Liu, “Size-dependent two-photon absorption in circular graphene quantum dots,” Opt. Express 24(3), 2877–2884 (2016).
[Crossref] [PubMed]

Lomeda, J. R.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Loss, D.

B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3(3), 192–196 (2007).
[Crossref]

Luo, K. Q.

X. T. Zheng, A. Ananthanarayanan, K. Q. Luo, and P. Chen, “Glowing graphene quantum dots and carbon dots: properties, syntheses, and biological applications,” Small 11(14), 1620–1636 (2015).
[Crossref] [PubMed]

Marchenkov, A. N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Massar, S.

Mayou, D.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Mccoubrey, K.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Mu, H.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Nakanishi, T.

T. Ando and T. Nakanishi, “Impurity Scattering in Carbon Nanotubes Absence of Back Scattering,” J. Phys. Soc. Jpn. 67(67), 1704–1713 (1998).
[Crossref]

Naud, C.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Park, J. H.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Pechprasarn, S.

P. Suvarnaphaet and S. Pechprasarn, “Graphene-based materials for biosensors: a review,” Sensors 17(10), 2161 (2017).

Ping, L. K.

Ponraj, J. S.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Price, B. K.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Qi, F.

F. Qi and G. Jin, “Strain sensing and far-infrared absorption in strained graphene quantum dots,” J. Appl. Phys. 114(7), 073509 (2013).
[Crossref]

Qi, S.

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

Qian, J.

J. Qian, M. Dutta, and M. A. Stroscio, “Phonon bottleneck effects in rectangular graphene quantum dots,” J. Comput. Electron. 11(3), 293–301 (2012).
[Crossref]

Rao, Z.

Q. Liu, B. Guo, Z. Rao, B. Zhang, and J. R. Gong, “Strong two-photon-induced fluorescence from photostable, biocompatible nitrogen-doped graphene quantum dots for cellular and deep-tissue imaging,” Nano Lett. 13(6), 2436–2441 (2013).
[Crossref] [PubMed]

Salomão, F. C.

F. C. Salomão, E. Lanzoni, C. Costa, C. Deneke, and E. B. Barros, “Determination of high frequency dielectric constant and surface potential of graphene oxide and influence of humidity by KPFM,” Languir 31(41), 11339–11343 (2015).
[Crossref] [PubMed]

Shin, D. H.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Shin, D. Y.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Silvestrov, P. G.

P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene,” Phys. Rev. Lett. 98(1), 016802 (2007).
[Crossref] [PubMed]

Sim, S.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Sinitskii, A.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Sone, C.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Song, Z.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Stormer, H. L.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Stroscio, M. A.

J. Qian, M. Dutta, and M. A. Stroscio, “Phonon bottleneck effects in rectangular graphene quantum dots,” J. Comput. Electron. 11(3), 293–301 (2012).
[Crossref]

Suvarnaphaet, P.

P. Suvarnaphaet and S. Pechprasarn, “Graphene-based materials for biosensors: a review,” Sensors 17(10), 2161 (2017).

Tan, Y. W.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Thakur, S.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Torre, B.

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

Tour, J. M.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Trauzettel, B.

B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3(3), 192–196 (2007).
[Crossref]

Virally, S.

Wang, Y.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Wang, Z.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Wu, H.

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

Wu, X.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Xiao, Q.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Xing, H.

T. Fang, A. Konar, H. Xing, and D. Jena, “Mobility in semiconducting graphene nanoribbons: Phonon, impurity, and edge roughness scattering,” Phys. Rev. B 78(20), 205403 (2008).
[Crossref]

Xu, X.

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

Xu, Y.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Xu, Z. Q.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Yang, S. B.

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Yu, X. F.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

Yuan, J.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Zeng, H.

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

Zhang, B.

Q. Liu, B. Guo, Z. Rao, B. Zhang, and J. R. Gong, “Strong two-photon-induced fluorescence from photostable, biocompatible nitrogen-doped graphene quantum dots for cellular and deep-tissue imaging,” Nano Lett. 13(6), 2436–2441 (2013).
[Crossref] [PubMed]

Zhang, H.

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

Zhang, R.

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

Zhang, Y.

J. S. Ponraj, Z. Q. Xu, S. C. Dhanabalan, H. Mu, Y. Wang, J. Yuan, P. Li, S. Thakur, M. Ashrafi, K. Mccoubrey, Y. Zhang, S. Li, H. Zhang, and Q. Bao, “Photonics and optoelectronics of two-dimensional materials beyond graphene,” Nanotechnology 27(46), 462001 (2016).
[Crossref] [PubMed]

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Zheng, X. T.

X. T. Zheng, A. Ananthanarayanan, K. Q. Luo, and P. Chen, “Glowing graphene quantum dots and carbon dots: properties, syntheses, and biological applications,” Small 11(14), 1620–1636 (2015).
[Crossref] [PubMed]

ACS Nano (1)

S. Kim, S. W. Hwang, M. K. Kim, D. Y. Shin, D. H. Shin, C. O. Kim, S. B. Yang, J. H. Park, E. Hwang, S. H. Choi, G. Ko, S. Sim, C. Sone, H. J. Choi, S. Bae, and B. H. Hong, “Anomalous behaviors of visible luminescence from graphene quantum dots: interplay between size and shape,” ACS Nano 6(9), 8203–8208 (2012).
[Crossref] [PubMed]

Adv. Opt. Mater. (1)

Y. Xu, Z. Wang, Z. Guo, H. Huang, Q. Xiao, H. Zhang, and X. F. Yu, “Solvothermal synthesis and ultrafast photonics of black phosphorus quantum dots,” Adv. Opt. Mater. 4(8), 1223–1229 (2016).
[Crossref]

J. Alloys Compd. (1)

R. Zhang, S. Qi, J. Jia, B. Torre, H. Zeng, H. Wu, and X. Xu, “Size and refinement edge-shape effects of graphene quantum dots on UV-visible absorption,” J. Alloys Compd. 623(6), 186–191 (2015).

J. Appl. Phys. (1)

F. Qi and G. Jin, “Strain sensing and far-infrared absorption in strained graphene quantum dots,” J. Appl. Phys. 114(7), 073509 (2013).
[Crossref]

J. Comput. Electron. (1)

J. Qian, M. Dutta, and M. A. Stroscio, “Phonon bottleneck effects in rectangular graphene quantum dots,” J. Comput. Electron. 11(3), 293–301 (2012).
[Crossref]

J. Phys. Soc. Jpn. (1)

T. Ando and T. Nakanishi, “Impurity Scattering in Carbon Nanotubes Absence of Back Scattering,” J. Phys. Soc. Jpn. 67(67), 1704–1713 (1998).
[Crossref]

Languir (1)

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Nat. Phys. (1)

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P. Suvarnaphaet and S. Pechprasarn, “Graphene-based materials for biosensors: a review,” Sensors 17(10), 2161 (2017).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of a monolayer rectangular GQD, the black and red circles are two type of carbon atoms A and B. a and b are unit vectors. (b) The reciprocal lattice.
Fig. 2
Fig. 2 Energy spectra of rectangular GQDs with different sizes as a function of kx.
Fig. 3
Fig. 3 Three energy states (1, 1), (1, 2) and (1, 3) of rectangular GQDs with varied M and a fixed N = 10.
Fig. 4
Fig. 4 Two-photon absorption spectra for non-3M0 sized GQDs plotted as a function of incident photon energy.
Fig. 5
Fig. 5 TPA spectra for 3M0-sized metallic rectangular GQDs with M = 9, 12, 15, 18 and N = 15, 20, 25. The dashed line is the TPA spectra contributed from the transitions between (1, n).

Equations (9)

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HΨ= v F ( 0 k x i k y 0 0 k x +i k y 0 0 0 0 0 0 k x +i k y 0 0 k x i k y 0 )( ψ A ψ B ψ A ' ψ B ' )=E( ψ A ψ B ψ A ' ψ B ' )
{ Ψ A (r)= e iΚr ψ A (r)+ e iΚ'r ψ A ' (r) Ψ B (r)= e iΚr ψ B (r)+ e iΚ'r ψ B ' (r) .
{ Ψ A (y=0)=0 Ψ B (y= L AC )=0
{ Ψ A (x=0)= Ψ A (x= L ZZ )=0 Ψ B (x=0)= Ψ B (x= L ZZ )=0 .
( ψ A ψ B ψ A ' ψ B ' )=( C e i k x x sin( k y y) C e i k x x sin( θ k + k y y) C e i k x x sin( k y y) C e i k x x sin( θ k + k y y) )
C= [ 2 L ZZ L AC + L ZZ sin(2 θ k )/ k y ] 1/2 .
E=± v F | k |=± v F k x 2 + k y 2
{ ( K 0 + k x ) L ZZ = m k π θ k + k y L AC = n k π
H v,i int = m 1 , n 1 |(e v F /c)Aσ| m 0 , n 0 = C 0 C 1 eA v F c L AC L ZZ 2 δ m 1 , m 0 ×{ e [ sin( n 0 π n 1 π+ θ k1 )sin θ k0 n 0 π θ k0 n 1 π+ θ k1 sin( n 0 π+ n 1 π θ k1 )sin θ k0 n 0 π θ k0 + n 1 π θ k1 ] + e + [ sin( n 1 π n 0 π+ θ k0 )sin θ k1 n 1 π θ k1 n 0 π+ θ k0 sin( n 1 π+ n 0 π θ k0 )sin θ k1 n 1 π θ k1 + n 0 π θ k0 ]}

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